Some moments of inertia for various shapes/objectsįor a uniform disk of radius r and total mass m the moment of inertia is simply 1/2 m r 2.Ī point particle of mass m in orbit at a distance r from an object has a moment of intertia of I=mr 2. Angular momentum in a closed system is a conserved quantity just as linear momentum P=mv (where m is mass and v is velocity) is a conserved quantity. The angular momentum of a solid object is just Iω where ω is the angular velocity in radians per second. You can think of the moment of inertia as the ability to resist a twisting force or torque.įor rotation about a fixed point, the moment of inertia of a body I is given by the sum of all the constituent particles masses m i multiplied by their radius r i from the fixed point squared. If the entire mass were concentrated at a point whose distance from the axis is equal to the radius of gyration k, the moment of inertia of the concentrated mass would be equal to that of the original mass. In Newtonian rotational physics angular acceleration is inversely proportional to the moment of inertia of a body. The radius of gyration k of a mass m about some axis is defined by. In Newtonian physics the acceleration of a body is inversely proportional to mass. The Moment of Inertia is often given the symbol I.
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